What parameter of the present universe, more than any other, is considered to be critical in determining the ultimate fate of the universe?
The question has been is the universe a closed system, an open system or a static system. If the density of the universe was exactly 1 then the universe would be a static system, the so called steady state universe. If the universe had a density of less than 1 then the universe would be a closed system undergoing alternating episodes of expansion (Big Bangs,) and contractions ( Big Crushes).
The increasing rate of expansion observed in 1998 indicates that the density of the universe is greater than 1. This means that the universe is an open system The conclusion is that the universe will continue to expand until maximum entropy is achieved. The result is the heat death of the universe.
The rate of the expansion of the universe is key in determining the density of the universe and its ultimate fate. The empirical evidence is that the fate of the universe will be the heat death. The universe is an open system and matter, and energy is not all that exists.